Thermal expansion of a shell

hi everybody
my question is:
a spherical shell is heated. the volume changes according to the equation V(T)=V(0)(1+yT) where y=volume coeff. of thermal expansion. does this volume refer to the volume enclosed by the shell or the volume of the material making up the shell?

Staff: Mentor

does this volume refer to the volume enclosed by the shell or the volume of the material making up the shell?

It doesn't matter. All volumes expand by the same fraction, whether you take the volume of the shell material or the volume enclosed by the shell. When the material expands, so does the volume it encloses.

let me put it in another way. if the shell of radius R has a spherical cavity of radius r, what will be the change in the two radii on heating? will the increase in both be 'aT' where a=linear coeff of thermal expansion?